paddlesports quick physics

Re: Percentages

– Last Updated: Jun-26-09 1:50 PM EST –

To quote Benford in ‘Naval Architecture for Non-Naval Architects’ 1991: “…the vessel’s turning center will seldom be found more than 20 percent of the vessel’s length from the bow, whereas the longitudinal center of gravity is usually somewhere near mid-length.”

You write that “The rule of thumb position of the pivot point when traveling at or around hull speed is one third of the distance along the keel at the waterline, measured back from the bow where it intersects the water. “ and “The phenomenon of the pivot point in displacement vessels is so well know and widely accepted (at least by professional mariners) that I suggest a search of the pertinent literature and some conversations with such persons, before looking for the forest between the trees, and before embarking on scientific research in what might not be such uncharted waters.”

I note that you have qualified your statement to read “when travelling at hull speed” which seems reasonable. If the pivot point moves from the CG forward once motion begins, surely it doesn’t instantly jump from 50% to 33%? If it winds up there at hull speed, so be it, although Benford disagrees on the location. One thing not mentioned in your article is the definition of the title: ‘Peripatetic Pivot Point’ – peripatetic means walking, or in terms of the pivot point, it moves around, so stating that it resides at a given position in general seems to be in error, but the hull speed qualification fixes that.

In the end, it seems the only thing widely accepted is that the effective turning center is forward of the CG – the assumed location obviously varies. I don’t have a problem with a rule of thumb (especially if it’s true), I’m just looking for a physical explanation. The several texts in Naval Arch that I’ve looked through don’t have one, but I will keep looking. The fact that it is well-accepted is fine, although I note that the concept of the ether was well-accepted in its day.

Per your suggestions, rest assured I am capable of calculating simple percentages. Also, as I am currently teaching the professional mariners of the future, I would like to be sure they are being taught physics, not anecdote. As far as my research plans, confirming and explaining (or denying) well-accepted bromides is one of the functions of experimental research, and a thorough literature search is the first step in any experiment. I don’t appreciate the implication that I am missing the forest for the trees – the fact that you can’t explain why the pivot point is where you say it is means there is work to be done.

It seems to this lay person that the PP
… residing at some point toward the bow, at speed, is the result of the chisel of the bow being driven into still water. Consequently the bow is the most firmly fixed part of the boat. Once the bow parts that water and gets it moving outward from the hull, the hull more easily moves side to side where the water is moving outward.

It seems pretty intuitive and easy to grasp, which could mean that it’s almost certainly incorrect. But I don’t think so.

Pivot Point…
I sure as hell think of it every time I’m pulling the 100ft boat under my command into the narrow slip with a 20 knot off-dock wind!

Re: percentages and more
I think everyone has learned and benefited from this discussion. I sure have. My previous note to you was a bit smartass, without justification, carldelo. It’s to your credit that you pursued the subject and shrugged off the offense.

Greyak has also made some comments that I think are really perceptive and productive about pressure differentials and about the different forces and the interactions of above and below waterline surfaces.

I have one additional comment on how the pivot point moves from the center of the waterline in a vessel making no way, to a point well forward in a vessel moving ahead at hull speed. I believe that the pivot point movement is not at all proportional to the speed. I believe that it moves quickly forward as the vessel begins to make headway. There almost certainly is an equation that describes the position of the pivot point in a displacement vessel primarily as a function of speed, and the relationship is not linear. (Other variables having a lesser effect have been suggested by other commentators.) My sense is that the pivot point moves rather quickly forward as the boat gains headway. And that is probably why I have not gotten farther, for practical purposes, than saying the pivot point is in the center when dead in the water, and pretty close to the ultimate location when moving forward (or aft) through the water.

Without more study on my part, I can’t contribute more. There are and have been excellent surmises, observations, reports, and analyses on this message board. Asserting the pivot point concept is a far cry from explaining it, but people commenting here are the only ones I have ever encountered who have asked the question and pursued answers to it (and the others related to the movement of a through water). So it’s all good, stimulating, and more. Thanks, everybody, for the challenging comments.

I do have two related questions.

First. Is a kayak or canoe that is surfing a displacement vessel, or has it become a planing vessel? (If it is planing, the pivot point no longer applies.)

Second. We know that the longer a canoe or kayak is, the faster it can go through the water (other things being equal). Can a really long canoe or kayak be paddled up “on step”? If enough strong paddlers are pushing a long enough boat, can it be planed? How fast can such a really long paddled boat be paddled? How long can it be kept up on step? I have heard that the European explorers sailing along the northern Pacific Coast of North America were startled when under full sail to be easily overtaken by, and left in the wake of, large dugout paddled canoes. And that the later “Yankee clipper” hull design was modeled on those incredible canoes.

Surfin’ a wave, yes, under paddle power no.

Posted recently on this. Under paddle power you’re talking about is “semiplaning” (not true planing) which most kayakers get really confused by, but you are likely familiar with. Since kayaks can exceed hull speed (S/L 1.34), they do operate in this mode - but usually only for Olympic K1 (S/l 2.2+), top surf ski racers, and the rest of us in short sprints occasionally. From 0 to HS draft increases, above HS it begins to back off and return to static level (and then even less and to actual planing mode on a wave, with a jet pack, etc.)

Fair enough

– Last Updated: Jun-27-09 12:10 AM EST –

If you (Clyde) read the article I linked to above, he echoes your view that the pivot point moves quite quickly from CG forward. As I mentioned above, he leaves the physics to Hooyer which I plan to peruse next week after I can get my mitts on it - I'll post back what I do or don't find.

I do think it's interesting that Benford (who I know is well regarded and whose book was published by SNAME) states that the pivot point is 20% back at most.

Now that I am home, I can access my copy of "The Shape of the Canoe" 3rd edition by John Winters. Hopefully he won't mind if I quote a short, germane passage:

"During the turn, the hull rotates about its center of gravity that, in obeying Newton’s first law of motion, attempts to continue along its original path. The bow describes a smaller arc than the CG and angles toward the inside the turning circle. Meanwhile, the stern describes a larger arc behind. To paddlers the boat appears to rotate about a point lying approximately twenty percent of the length aft of the bow (the precise point varies with hull configuration, heel, trim, etc.). The flow of water across the hull and the drift angle (sideslip) causes this illusion. Since the boat rotates about its CG, the force moments causing the turn determine the rate and radius of the turn. Increasing the lateral resistance forward by trimming down by the bow or using a control stroke increases the turn rate and decreases the turn radius. Increasing the lateral resistance aft, say by trimming down by the stern, decreases the turn rate and increases the radius."

So he does in fact refute the moving pivot point - very interesting, and it ties in with the 20% value given by Benford. It will be interesting to see what Hooyer says - stay tuned.

Re: planing (or semi-planing, per Grayak), a 5m long kayak is in the semi-planing regime (Froude number 0.4-0.6) from about 5.5 to 8 knots. I recently read accounts of Aleuts paddling Baidarka at 10 knots for times, to the extent that some paddlers later died from the exertion. The tales are related in "Form & Function of the Baidarka: the Framework of Design" by George Dyson - those Aleut were some tough guys, I guess.

When static surfing a wave
It sure seems like the pivot point is forward of the CG. I don’t think it’s illusion. Maybe that surfing phenomenon is completely different than what is being discussed. Or, maybe the bow is being pinned in both scenarios.

The more key points…
… are that Winters is saying this an apparent phenomenon only, and also that the perceived point varies based on several things.

The point doesn’t actually physically exist, it’s an illusion, so likely tilting at windmills here as far as isolating it via some formula.

The bow arc being smaller than stern arc as he describes is dependent on forward speed, no? A kayak doing a flat spin has about same arcs, when moving they’re quite different. Gets us back to the same “variable” thing as far as the apparent point’s location.

Perception of this point would sort of “jump” out there pretty quick, as there’s a big apparent difference from 0 speed spin to even a slow speed turn, and then less difference beyond as all the arcs get larger at higher speeds and so less additional apparent difference.

So does this mean that…
… even though the PP is an illusion you still need to act as if it isn’t or you will be unable to dock your 100’ boat?

Yeah, that’s about how I’m seeing it NM

Seems reasonable
I realized that yesterday while I was doing a close-quarter 180 to get my boat up to the dock in some wind waves, I was definitely maneuvering as if the pivot was moving - stern sweep at slow ahead, bow sweep at slow reverse - I guess I’ve been using the fact without realizing it. go figure.

safe passage through quoted words

– Last Updated: Jun-30-09 7:26 PM EST –

regarding the quoted passage attributed to "the Shape of the Canoe":

There are several glaring fallacies in the quoted passage. The worst (repeated twice in that one paragraph) is that the hull rotates about its center of gravity. Let me plainly state that a displacement vessel making way through water, and subsequently changing its heading, does NOT rotate about its center of gravity, and there is nothing in the laws of physics that requires it to do so.

The author even suggests evidence against his own assertions. It is quite impossible for the bow to move through a smaller arc than the stern, if the vessel is actually pivoting around the center of gravity (which this discussion certainly assumes is at or very near the fore-and-aft center of the vessel, amidships). It's quite elementary.

It is also a severe enough distortion of Newton's Laws to make untrue the assertion that a center of gravity "attempts to continue along its original path". What if the "original path" is along the arc of a circle, for instance? There is no law of physics that will encourage it to continue that path without an introduced outside force acting upon it. Also, not much sense at all can be made of a claim that a center of gravity "attempts" to do anything.

The author is also quite arbitrary (and unjustified) in asserting that a center of gravity is somehow a substantial, real thing, whereas a pivot point is merely an "illusion" that "the boat appears to rotate about", thus fooling gullible recreational paddlers (to say nothing of naive professional seafarers around the world for thousands of years).

The Law of Gravity itself is a mathematical abstraction (or description, if you will) of observed phenomena. Does anyone yet know what gravity really is? A "center of gravity" is at least as much of an illusion as is a peripatetic pivot point. We can closely observe the rotation of a material object, and thus can clearly and precisely identify the center of rotation. The center of gravity of a real object is more difficult to observe and identify with certainty, especially if it's composition is not uniform and its geometry is complex. Engineers and physicists can tell you the point that a boat is rotating about much more easily than they can locate it's center of gravity (whatever that is).

I'm not saying that a boat doesn't have a center of gravity. But it is preposterous to say that a boat always rotates about its center of gravity. And it is beyond absurd to say that the point about which a boat rotates when changing heading while underway is no more than an illusion that fools everyone but the author.

Refuting the peripatetic pivot point with unfounded, erroneous but scientific sounding statements just won't hold water.

You can paddle a boat, and even design a boat, without understanding Newtonian physics or the basic principles of hydrodynamics. And conversely, paddling or designing canoes doesn't make you an authority on those subjects, either.

aleut surfers
Tough they certainly were, but they were also terrorized. Russian private traders, licensed like corporations by the czar, were unregulated, ruthless, well-armed, and experienced in decimation, torture, and holding loved ones hostage. If an Aleut didn’t comply, he or she, or family members, or the entire village, died cruelly and violently. And paddling and hunting under orders that could not be questioned, from the Aleutian chain to California, including across the Gulf of Alaska, in one, two, or three hole kayaks, meant that paddling for one’s life was a normal experience.

I still wonder whether it is known whether the 60 foot dugouts of the Tlingit, Haida, Tsimshian, Kwakiutl, and other peoples, used for whaling, trading, potlatching, moving, and waring, were able to achieve and maintain planing speeds. Similarly, were the large trading birchbark canoes of over thirty feet and more, employed on the Great Lakes, able to get up and stay up on step for long distances?

There is (is there not?) less power consumed per mile while planing than while in displacement mode. On the other hand, if planing speed is greater than the speed at which a paddle rapidly wielded can be stroked, then it would seem impossible to paddle a boat on step, regardless of the amount of power available. A longer paddle can provide a quicker stroke, but there are still limits.

Those speed accounts are pre-Russian…

– Last Updated: Jul-01-09 4:45 AM EST –

... (at least what I've read, and Carl now owns most of my books so can't cite) so their reported performance had nothing to do with Russian business practices or any atrocities thereof.

The Baidarkas from the Russian trapper era, while capable craft in their own right - were modified for the task at hand which was hauling a lot of fur bearing sea mammals as well as Russian non-paddlers (why there ever was a three holer) while also being supported by and carried long distance by ship. These types became somewhat standardized and pretty much wiped out earlier and more varied types. These later types are not in the same performance league as the earlier single baidarkas that plied the seas before this, and that are all but lost to history save the few early accounts of them pacing sailing ships (that could measure and knew their own speed through the water, and were both amazed and perplexed by these odd craft).

Study of Aleut skeletons also show bone sizes and densities consistent with powerful physiques and potential to be exceptional paddlers (as in Olympic caliber plus).

Tom Foster and others of the ACA use the terms “frontal resistance” end and “eddy resistance end” to describe the two ends of the boat traveling through water.

Intuitively, if you lean forward or paddle forward hard you make the bow “sticky” and make the stern “loose”.

Who cares if it’s wrong? If the mental concept adequately explains natural phenomena it’s useful as a first-order approximation. Issac Newton’s theories explained a heck of a lot before Albert Einstein came along.

I’ll echo each of Greyak’s points here, based on the very substantial kayak reference library he passed on to me. The high speeds reported were in early craft being seen by western explorers for the first time, it was not a ‘paddle or die’ situation.

Sorry Clyde, but there are no errors in John Winters’ passage - they are all factually and conceptually correct.

The center of gravity of an object is quite real, and quite easy to determine in practice. Give me a boat, paddler and two bathroom scales and I can find the 3-D location of the CG in a few minutes.

However, the location of the effective center of rotation of a body depends entirely on the frame of reference being considered. The apparent rotation center will be different if you are sitting in the boat (moving reference frame) versus moving with the water (different moving reference frame) or on dry land observing a moving boat on moving water (fixed or inertial reference frame).

Specifically, if you are in the boat and it is following a curved path, you are in a non-inertial reference frame and the Newtonian laws do weird things. This is quite difficult to explain without a blackboard and some vector expressions.

At any rate, the location of the peripatetic pivot point that you speak of is taken from the paddler’s (or ship pilot’s) perspective, i.e. in a moving reference frame. This is obviously useful from a ship maneuvering point of view.

For a fixed observer, the motion of the boat is better expressed in terms of rotation about the CG superposed with translation of the CG in a given direction (possibly a circular path). These two concepts are not in conflict, they are different methods of describing the motion of the boat. The figure Greyak cites (or one similar) is always included in basic Naval Arch texts - it clearly describes the motion in the context of an inertial reference frame, based on the CG of the boat.

When J. Winters says the CG attempts to move along its original path, he means in a straight line, which is what Newton’s first law is all about. There is nothing impossible about his description of the bow and stern describing arcs of different radii - an example:

Consider a boat ‘circling the drain’, moving in a constant radius circle with the bow always pointing to the center. The boat is simultaneously rotating about its CG, while the CG is rotating about the drain and the bow and stern describe arcs of quite different radius. So what is the center of rotation here? For an outside observer, you could argue as I did above that the boat is rotating about its CG which in turn revolves about the drain. Or you could say the boat as a whole is in solid-body rotation about the drain itself. This is called the ‘instantaneous center of rotation’ and is an equally valid description.

From the point of view of the paddler, the stern is displacing quite a bit, while the bow moves less (because of the smaller radius). So I guess he would necessarily perceive the center of rotation somewhere in the front half of the boat - how far from center depends on the actual radius of the boats motion, which changes the differential between the bow and stern. Therefore, the apparent center of rotation for the paddler moves (peripatetic) and depends on the overall distance of the CG from the instantaneous center of rotation, combined with the boats rotation rate about the CG itself. In this example, the rotation rate about the CG and the drain are linked, but this is not generally the case.

Finally, there’s nothing wrong with anthropomorphizing the laws of physics (‘the CG attempts…’), I do it for my students all the time as it helps with visualization of the problem.

This is much longer than I meant, but I think I got to the main points, and as it is summer, I believe I will spare myself the vector math to prove it all (until the fall maybe).

Re: Sorry
You shoulda checked first before asserting in your criticism that “there are no errors in John Winters’ passage - they are all factually and conceptually correct”. Oh, my! That single paragraph passage contains the statement that "During the turn, the hull rotates about its center of gravity … ", and later in that same paragraph, “Since the boat rotates about its CG …”. There are others, but this will suffice.

You see, the CG (like every other point on the vessel, including the peripatetic pivot point) rotates (approximately) about something called the “center of the turning radius”, which is outside the vessel. But every point on the turning vessel with headway (including the CG) also rotates about the peripatetic pivot point. The CG, under these turning conditions, is not the center of any rotation.

The serious problem with those two “Shape of the Canoe” assertions (as quoted by carldelo in “Fair enough”,and excerpted in the first paragraph above) is that Newtons Laws state that a body rotates about its center of gravity when it is rotating freely and not acted upon by other forces. A vessel traveling through water at a constant speed and in a straight line is being acted upon by forces that are in balance, but not symmetrical. Such a moving vessel, when it initiates and continues a turn in water, is not rotating freely, and is indeed being acted upon, throughout, by changing and unbalanced forces. That’s why it can and does rotate in fact and in reality about a pivot point that is not at the same location as the center of gravity. It has nothing to do with appearances, illusions, psychology, relativity vs classical mechanics, or the perspective of an observer. All of these have been postulated in this thread in order for preconceived mistaken notions, and published statements made by favored writers to squirm free. I say again, a displacement vessel, making headway, and changing its heading, does NOT rotate about its own center of gravity. The vessel rotates about the pivot point of the vessel, which is determined by the totality of forces applied to the vessel, and which is typically located well forward of the center of gravity (as described elsewhere by Hooyer and others - including me).

If by some magic, the environment surrounding the vessel turning and making way through the water were to instantly disappear, and the vessel were weightless and in space, with no external forces applied to the hull, the ship would sail off in a (Newtonian) straight line on the course and speed she was making at the instant the environment was transformed, and she would conserve the rotational momentum she had at that moment, spinning off into a space odyssey, revolving forever about her new pivot point which would, of course, now, finally, and forever be located at her center of gravity. Excuse me - center of mass.

(Sorry for distracting you with the fantastical image, but it’s more fun than imagining going down the drain, ain’a?)

More (including, unfortunately, the preceding spacey paragraph) would only distract us all from the point of this discussion, which is that the turning vessel making headway does not (as alleged by others in this thread) pivot around its center of gravity. The CG travels in a more or less circular path around the center (outside of the vessel perimeter) of something called the turning circle, and the CG (as well as every other point on the vessel) also revolves around something (inside of the vessel perimeter) called the peripatetic pivot point, which is located well forward of midships and the CG.

Knowledge of both motions is extremely valuable and helpful in effective handling of a displacement vessel of any size. Most paddlers know something constructive about the turning circle. That is not true of the peripatetic pivot point. That has been my motivation in writing my article about it, and in commenting exhaustively here. I have not been seeking to explore and digress into the nuances of physics and hydrodynamics. Just looking for what is true and for the simple truth that helps.

Remember, folks. The boat cannot pivot (revolve, spin, what have you) around two different points on the boat at the same time. It either pivots around the peripatetic pivot point, or it pivots (as JW and greyak and carldelo have said) around the center of gravity. I guess you can take your choice - or find out what’s true. And here’s a bonus: The location of the pivot point is irrespective of whether the observer is on the boat, floating in the water, on the beach, hovering overhead, or not even watching. But since you’re probably either operating the boat, or about to get run over by a part of it, your perspective is an important one.

speed and ditto head
I don’t have the benefit of that very substantial kayak reference library, so please clarify, which pre-Russian Europeans “discovered” the Aleutian Islands and the Bering Sea, and clocked the Aleuts before the Russians got there? It wasn’t Cook. If memory serves (and that’s all I’ve been going on) Cook got as far as, uh, Cook Inlet. (Which was a fur piece.) Maybe Vitus Bering did it. I don’t think he was born in Russia. Nevertheless, he was sailing for the Russians, sailing with Russians. I think. Could have been anyone, but I’d lay odds that Veniaminoff clocked the Aleuts (or asked that it be done).

Veniaminoff and Bering accompanied the Russian chartered privateers, as I recall. Veniaminoff as priest and anthropologist/linguist. Bering as governor.

But my curiosity still persists about whether those 30 to 60 foot Northwest Coast dugouts and Great Lakes birchbark canoes, were/are able to get up on step and plane. If planing speed is greater than the speed that a team of bodacious paddlers can slap the water with their long shafted paddles, then it can’t be done, with paddles, regardless of whether the team has the collective power to (theoretically) propel the canoe to the required speed.

anyone who says
"The phenomenon … is so well know and widely accepted … that I suggest a search of the pertinent literature"

should provide a bibliography of sources used. In fact, anyone who uses others ideas should site their sources. Give credit where credit is due.